If the lines $ \frac{x-1}{-3}=\frac{y-2}{2 k}=\frac{z-3}{2}, \frac{x-1}{3 k}=\frac{y-5}{1}=\frac{z-6}{-5} $ are at right angles, then $ k= $

Question

If the lines $ \frac{x-1}{-3}=\frac{y-2}{2 k}=\frac{z-3}{2}, \frac{x-1}{3 k}=\frac{y-5}{1}=\frac{z-6}{-5} $ are at right angles, then $ k= $, $ -10 $, $ \frac{10}{7} $, $ \frac{-10}{7} $, $ \frac{-7}{10} $

MARKS App · Accepted Answer

Lines are perpendicular if a 1 a 2 + b 1 b 2 + c 1 c 2 = 0 Hence, - 3 3 k + 2 k 1 + 2 - 5 = 0 ⇒ k = - 10 7 .

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